Professor Angela Mihai

Teams and roles for Angela Mihai

Professor of Applied Mathematics
School of Mathematics

I am a member of the Applied and Computational Mathematics Research Group and a Fellow of the Institute of Mathematics and its Applications (FIMA).

I enjoy formulating and solving mathematical problems to answer important questions in science, engineering, and everyday life. It also gives me pleasure to discover new mathematical approaches and ask further questions along the way. A very exciting line of enquiry is how a mathematical model or technique can be translated from one field of application to another, and the interdisciplinary insight this brings is often highly rewarding.

2025

Liu, Y., Goriely, A. and Mihai, L. A. 2025. Elephant trunk wrinkles: A mathematical model of function and form. Nonlinearity 38(3), article number: 35004. (10.1088/1361-6544/adaf6c)

2024

Poudel, R., Sengul, Y. and Mihai, L. A. 2024. Deformation localisation in stretched liquid crystal elastomers. Mechanics of Soft Materials 6, article number: 8. (10.1007/s42558-024-00063-2)
Mihai, L. A. and Goriely, A. 2024. Controllable deformations of unconstrained ideal nematic elastomers. Journal of Elasticity 156(1), pp. 95-106. (10.1007/s10659-023-10038-5)
Mihai, L. A. 2024. A mathematical mechanics mixed tape: Editor's foreword to special issue in honor of Alain Goriely. Mathematics and Mechanics of Solids 29(6), pp. 1049-1052. (10.1177/10812865231210188)
Mihai, L. A. 2024. A theoretical model for power generation via liquid crystal elastomers. Mathematics and Mechanics of Solids 29(6), pp. 1198-1215. (10.1177/10812865231193735)
Mahardika, N., Raistrick, T., Mihai, L. A. and Wang, H. 2024. All-atom molecular dynamics simulations of nematic liquid crystal elastomers. International Journal of Solids and Structures 291, article number: 112717. (10.1016/j.ijsolstr.2024.112717)

2023

Mihai, L. A. 2023. A theoretical liquid crystal elastomer model that mimics the elasticity of cat skin. Mechanics of soft materials 5, article number: 4. (10.1007/s42558-023-00051-y)
Mihai, L. A., Raistrick, T., Gleeson, H. F., Mistry, D. and Goriely, A. 2023. A predictive theoretical model for stretch-induced instabilities in liquid crystal elastomers. Liquid Crystals 50(7-10), pp. 1426-1438. (10.1080/02678292.2022.2161655)
Mihai, L. A., Gablier, A., Terentjev, E. and Goriely, A. 2023. Anti-Hertz bulging of actuated liquid crystal elastomers. Extreme Mechanics Letters 64, article number: 102066. (10.1016/j.eml.2023.102066)
Goriely, A., Moulton, D. E. and Mihai, L. A. 2023. A rod theory for liquid crystalline elastomers. Journal of Elasticity 153, pp. 509-532. (10.1007/s10659-021-09875-z)

2022

Mihai, L. A., Mistry, D., Raistrick, T., Gleeson, H. F. and Goriely, A. 2022. A mathematical model for the auxetic response of liquid crystal elastomers. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 380, article number: 20210326. (10.1098/rsta.2021.0326)
Buze, M., Woolley, T. E. and Mihai, L. A. 2022. A stochastic framework for atomistic fracture. SIAM Journal on Applied Mathematics 82(2), pp. 526-548. (10.1137/21M1416436)
Mihai, L. A. 2022. Stochastic elasticity: a nondeterministic approach to the nonlinear field theory. Interdisciplinary Applied Mathematics. Switzerland: Springer. (10.1007/978-3-031-06692-4)

2021

Mihai, L. A. and Goriely, A. 2021. Instabilities in liquid crystal elastomers. MRS Bulletin 46, pp. 784-794. (10.1557/s43577-021-00115-2)
Mihai, L. A., Wang, H., Guilleminot, J. and Goriely, A. 2021. Nematic liquid crystalline elastomers are aeolotropic materials. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 477(2253), article number: 20210259. (10.1098/rspa.2021.0259)
Goriely, A. and Mihai, L. A. 2021. Liquid crystal elastomers wrinkling. Nonlinearity 34(8), article number: 5599. (10.1088/1361-6544/ac09c1)
Mihai, L. A. and Alamoudi, M. 2021. Likely oscillatory motions of stochastic hyperelastic spherical shells and tubes. International Journal of Non-Linear Mechanics 130, article number: 103671. (10.1016/j.ijnonlinmec.2021.103671)

2020

Mihai, L. A. and Goriely, A. 2020. A plate theory for nematic liquid crystalline solids. Journal of the Mechanics and Physics of Solids 144, article number: 104101. (10.1016/j.jmps.2020.104101)
Mihai, L. A. and Goriely, A. 2020. A pseudo-anelastic model for stress softening in liquid crystal elastomers. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476(2243), article number: 20200558. (10.1098/rspa.2020.0558)
Mihai, L. A. and Goriely, A. 2020. Likely striping in stochastic nematic elastomers. Mathematics and Mechanics of Solids 25(10), pp. 1851-1872. (10.1177/1081286520914958)
Mihai, L. A., Woolley, T. and Goriely, A. 2020. Likely cavitation and radial motion of stochastic elastic spheres. Nonlinearity 33(5), article number: 1987. (10.1088/1361-6544/ab7104)
Schweickert, E., Mihai, L. A., Martin, R. J. and Neff, P. 2020. A note on non-homogeneous deformations with homogeneous Cauchy stress for a strictly rank-one convex energy in isotropic hyperelasticity. International Journal of Non-Linear Mechanics 119, article number: 103282. (10.1016/j.ijnonlinmec.2019.103282)

2019

Fitt, D., Wyatt, H., Woolley, T. and Mihai, L. A. 2019. Uncertainty quantification of elastic material responses: testing, stochastic calibration and Bayesian model selection. Mechanics of Soft Materials 1, article number: 13. (10.1007/s42558-019-0013-1)
Mihai, L. A. 2019. Power in numbers: The rebel women of mathematics by Talithia Williams [Book Review]. London Mathematical Society Newsletter 485, pp. 49-50.
Mihai, L. A., Fitt, D., Woolley, T. and Goriely, A. 2019. Likely cavitation in stochastic elasticity. Journal of Elasticity 137(1), pp. 27-42. (10.1007/s10659-018-9706-1)
Mihai, L. A., Woolley, T. and Goriely, A. 2019. Likely chirality of stochastic anisotropic hyperelastic tubes. International Journal of Non-Linear Mechanics 114, pp. 9-20. (10.1016/j.ijnonlinmec.2019.04.004)
Mihai, L. A., Fitt, D., Woolley, T. E. and Goriely, A. 2019. Likely equilibria of stochastic hyperelastic spherical shells and tubes. Mathematics and Mechanics of Solids 24(7), pp. 2066-2082. (10.1177/1081286518811881)
Mihai, L. A., Woolley, T. E. and Goriely, A. 2019. Likely equilibria of the stochastic Rivlin cube. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 377(2144), article number: 20180068. (10.1098/rsta.2018.0068)
Mihai, L., Fitt, D., Woolley, T. and Goriely, A. 2019. Likely oscillatory motions of stochastic hyperelastic solids. Transactions of Mathematics and Its Applications 3(1), article number: tnz003. (10.1093/imatrm/tnz003)
Wyatt, H., Safar, A., Clarke, A., Evans, S. and Mihai, L. A. 2019. Nonlinear scaling effects in the stiffness of soft cellular structures. Royal Society Open Science 6(1), article number: 181361.

2018

Schweickert, E., Mihai, L. A. and Neff, P. 2018. Homogeneous Cauchy stress induced by non-homogeneous deformations. Presented at: 89th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Munich, Germany, 19-23 March 2018. Proceedings in Applied Mathematics and Mechanics (PAMM) Vol. 1. Wiley pp. 1-2., (10.1002/pamm.201800185)
Safar, A. and Mihai, L. A. 2018. The nonlinear elasticity of hyperelastic models for stretch-dominated cellular structures. International Journal of Non-Linear Mechanics 106, pp. 144-154. (10.1016/j.ijnonlinmec.2018.08.006)
Mihai, L. A., Safar, A. and Wyatt, H. L. 2018. Debonding of cellular structures with fibre-reinforced cell walls under shear deformation. Journal of Engineering Mathematics 109(1), pp. 3-19. (10.1007/s10665-016-9894-2)
Mihai, L. A. and Neff, P. 2018. Hyperelastic bodies under homogeneous Cauchy stress induced by three-dimensional non-homogeneous deformations. Mathematics and Mechanics of Solids 23(4), pp. 606-616. (10.1177/1081286516682556)
Mihai, L. A., Woolley, T. and Goriely, A. 2018. Stochastic isotropic hyperelastic materials: constitutive calibration and model selection. Proceedings of the Royal Society A 474(2211), article number: 201708. (10.1098/rspa.2017.0858)

2017

Mihai, L. A. and Goriely, A. 2017. How to characterize a nonlinear elastic material? A review on nonlinear constitutive parameters in isotropic finite elasticity. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473(2207), article number: 607. (10.1098/rspa.2017.0607)
Mihai, L. A., Budday, S., Holzapfel, G., Kuhl, E. and Goriely, A. 2017. A family of hyperelastic models for human brain tissue. Journal of the Mechanics and Physics of Solids 106, pp. 60-79. (10.1016/j.jmps.2017.05.015)
Mihai, L. A., Wyatt, H. and Goriely, A. 2017. A microstructure-based hyperelastic model for open-cell solids. SIAM Journal on Applied Mathematics 77(4), pp. 1397-1416. (10.1137/16M1098899)
Safar, A., Wyatt, H. L. and Mihai, L. A. 2017. Debonding of cellular structures under shear deformation. Presented at: 25th Conference of the UK Association for Computational Mechanics, University of Birmingham, Birmingham, UK, 11-13 April 2017.
Mihai, L. A., Wyatt, H. L. and Goriely, A. 2017. Microstructure-based hyperelastic models for closed-cell solids. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473(2200), article number: 20170036. (10.1098/rspa.2017.0036)
Lee, C., Mihai, L. A., Hale, J. S., Kerfriden, P. and Bordas, S. P. A. 2017. Strain smoothing for compressible and nearly-incompressible finite elasticity. Computers & Structures 182, pp. 540-555. (10.1016/j.compstruc.2016.05.004)
Neff, P. and Mihai, L. A. 2017. Injectivity of the Cauchy-stress tensor along rank-one connected lines under strict rank-one convexity condition. Journal of Elasticity 127(2), pp. 309-315. (10.1007/s10659-016-9609-y)
Mihai, L. A. and Neff, P. 2017. Hyperelastic bodies under homogeneous Cauchy stress induced by non-homogeneous finite deformations. International Journal of Non-Linear Mechanics 89, pp. 93-100. (10.1016/j.ijnonlinmec.2016.12.003)
Mihai, L. A. 2017. The ascent of Mary Somerville in 19th century society by Elisabetta Strickland [Book Review]. London Mathematical Society Newsletter March(467), pp. 29-30.
Wyatt, H. L., Clarke, A., Evans, S. L. and Mihai, L. A. 2017. Optical strain measurement techniques for soft cellular structures. Presented at: BSSM 12th International Conference on Advances in Experimental Mechanics, Sheffield, UK, 29 - 31 August 2017.
Mihai, L. A., Alayyash, K. and Wyatt, H. L. 2017. The optimal density of cellular solids in axial tension. Computer Methods in Biomechanics and Biomedical Engineering 20(7), pp. 701-713. (10.1080/10255842.2017.1292352)

2016

Wyatt, H. L., Alayyash, K., Evans, S. L. and Mihai, L. A. 2016. Computer modelling of cellular structures under uniaxial loading. Presented at: 24th Conference of the UK Association on Computational Mechanics, Cardiff University, Cardiff, UK, 31 March - 1 April 2016. Cardiff: pp. 184-187.
Mihai, L. A. and Goriely, A. 2016. Guaranteed upper and lower bounds on the uniform load of contact problems in elasticity. Siam Journal on Applied Mathematics 76(4), pp. 1558-1576. (10.1137/15M1046563)
Wyatt, H. L., Alayyash, K. and Mihai, L. A. 2016. Optimising material density of cellular bodies in high elastic deformations. Presented at: 24th International Congress of Theoretical and Applied Mechanics, Montreal, Canada, 21-25 August 2016.

2015

Mihai, L. A., Chin, L., Janmey, P. A. and Goriely, A. 2015. A comparison of hyperelastic constitutive models applicable to brain and fat tissues. Journal of the Royal Society Interface 12(110), pp. -., article number: 20150486. (10.1098/rsif.2015.0486)
Mihai, L. A., Alayyash, K. and Goriely, A. 2015. Paws, pads, and plants: The enhanced elasticity of cell-filled load-bearing structures. Proceedings of the Royal Society of London Series A 471(2178), article number: 20150107. (10.1098/rspa.2015.0107)
Mihai, L. A. and Goriely, A. 2015. Finite deformation effects in cellular structures with hyperelastic cell walls. International Journal of Solids and Structures 53, pp. 107-128. (10.1016/j.ijsolstr.2014.10.015)

2014

Mihai, L. A. and Goriely, A. 2014. Nonlinear Poisson effects in soft honeycombs. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470(2169), article number: 20140363. (10.1098/rspa.2014.0363)

2013

Mihai, L. A. 2013. Cardiff students hold first SIAM Chapter Day. SIAM News 2013(1 Apr)
Mihai, L. A. and Goriely, A. 2013. Numerical simulation of shear and the Poynting effects by the finite element method: An application of the generalised empirical inequalities in non-linear elasticity. International Journal of Non-Linear Mechanics 49, pp. 1-14. (10.1016/j.ijnonlinmec.2012.09.001)

2011

Mihai, L. A. and Goriely, A. 2011. Positive or negative Poynting effect? The role of adscititious inequalities in hyperelastic materials. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 467(2136), pp. 3633-3646. (10.1098/rspa.2011.0281)

2010

Mihai, L. A. 2010. A fixed-point approach to the limit load analysis of multibody structures with Coulomb friction. Computers & Structures 88(13-14), pp. 859-869. (10.1016/j.compstruc.2010.04.005)

2009

Mihai, L. A. and Craig, A. W. 2009. Alternate slice-based substructuring in three dimensions. Ima Journal of Numerical Analysis 29(3), pp. 508-538. (10.1093/imanum/drn023)
Ainsworth, M. and Mihai, L. A. 2009. An adaptive multi-scale approach to the modelling of masonry structures. International Journal for Numerical Methods in Engineering 78(10), pp. 1135-1163. (10.1002/nme.2520)
Mihai, L. A. and Ainsworth, M. 2009. An adaptive multi-scale computational modelling of Clare College Bridge. Computer Methods in Applied Mechanics and Engineering 198(21-26), pp. 1839-1847. (10.1016/j.cma.2008.12.030)
Mihai, L. A. and Ainsworth, M. 2009. A finite element procedure for rigorous numerical enclosures on the limit load in the analysis of multibody structures. Computer Methods in Applied Mechanics and Engineering 199(1-4), pp. 48-60. (10.1016/j.cma.2009.09.018)

2007

Ainsworth, M. and Mihai, L. A. 2007. Modeling and numerical analysis of masonry structures. Numerical Methods for Partial Differential Equations 23(4), pp. 798-816. (10.1002/num.20253)

2006

Mihai, L. A. and Craig, A. W. 2006. Alternate strip-based substructuring algorithms for elliptic PDEs in two dimensions. Ima Journal of Numerical Analysis 26(2), pp. 354-380. (10.1093/imanum/dri025)
Ainsworth, M. and Mihai, L. A. 2006. A comparison of solvers for linear complementarity problems arising from large-scale masonry structures. Applications of Mathematics 51(2), pp. 93-128. (10.1007/s10492-006-0008-8)

2005

Mihai, L. A. and Craig, A. W. 2005. A two-grid alternate strip-based domain decomposition strategy in two-dimensions. In: Kornhuber, R. et al. eds. Domain Decomposition Methods in Science and Engineering. Springer-Verlag Berlin Heidelberg, pp. 661-668., (10.1007/3-540-26825-1_71)

I have broad research interests in applied and computational mathematics at the interface with physical and natural sciences. My expertise is in fundamental solid mechanics and the mathematical understanding of soft materials, including multiscale modelling, limit states analysis, optimisation, and uncertainty quantification.

I led externally funded research projects on cellular solids and multi-body systems with applications to biological tissues and soft matter, and made contributions to stochastic elasticity, which is a fast-developing field at the forefront of interdisciplinary research in continuum mechanics.

My research monograph, “Stochastic Elasticity: A Nondeterministic Approach to the Nonlinear Field Theory”, Springer, 2022, is the first book to combine fundamental large strain elasticity and probability theories. Its aim is to make both theories accessible to scientists wishing to incorporate uncertainty quantification in phenomenological studies of soft materials. It is a modern book that covers classical and more advanced research topics.

An important area of my work is the mathematical modelling of liquid crystal elastomers (LCEs). These are advanced multifunctional materials that combine elasticity with orientational order. Specifically, mechanical strains give rise to changes in liquid crystalline order and changes in the orientational order generate mechanical stresses and strains. Because of their complex material responses in the presence of natural stimuli like heat, light, electric or magnetic fields, LCEs are suitable for a wide range of applications in science, manufacturing, and medical research. This work provides the foundation for further mathematical modelling of self-organisation in active biological matter.

Visit Google Scholar, MathSciNet, ORCID, and ResearchGate

Funded projects

Learning macroscopic models for multibody systems of hyperelastic materials, International Centre for Mathematical Sciences (ICMS), Edinburgh (2024), Research in groups supported by EPSRC Grant EP/R015007/1 to ICMS
Pattern formation in soft materials: reduced models and nonlinear analysis, HORIZON-MSCA-2022 Postdoctoral Fellowship to Dr Yang Liu, University of Oxford, UK (2023 - 2025)
Uncertainty quantification and stochastic modelling of materials, Issac Newton Institute for Mathematical Sciences, Cambridge (2023), Research programme supported by EPSRC Grant EP/R014604/1to INI
Mathematical modelling and numerical analysis of liquid crystal elastomers, Full PhD studentship, College of Physical Sciences and Engineering, Cardiff University (2022 - 2026)
Limit analysis of debonding states in multi-body systems of stochastic hyperelastic material, EPSRC Grant EP/S028870/1 (2019 - 2022)
Debonding and stretching of biogenic cellular structures, Full PhD studentship, College of Physical Sciences and Engineering, Cardiff University (2015 - 2019)
Limit analysis of collapse states in cellular solids, EPSRC Grant EP/M011992/1 (2015 - 2017)

Special events organisation

Retreat for women in applied mathematics, International Centre for Mathematical Sciences (ICMS), Edinburgh (2025), Strategic workshop supported by EPSRC Grant EP/Z000467/1 to ICMS
Retreat for women in applied mathematics, International Centre for Mathematical Sciences (ICMS), Edinburgh (2024), Strategic workshop supported by EPSRC Grant EP/R015007/1 to ICMS
Retreat for women in applied mathematics, International Centre for Mathematical Sciences (ICMS), Edinburgh (2023), Strategic workshop spported by EPSRC Grant EP/R015007/1 to ICMS

Video recordings

Liquid crystal elastomers: theory and applications, International Centre for Mathematical Sciences (January 2024)
Uncertainty quantification and stochastic modelling of materials: Organiser interview, Isaac Newton Institute (August 2023)
Instabilities in liquid crystal elastomers, Isaac Newton Institute (July 2023)
Mathematics and mechanics of liquid crystal elastomers, Journal of Engineering Mathematics Webinar (October 2022)
Mathematics and mechanics of liquid crystal elastomers, Cardiff Applied and Computational Mathematics Seminar (November 2021)
The mathematics and continuum mechanics of liquid crystal elastomers, LMS Prospects in Mathematics (September 2021)
Women in STEM, Cardiff (March 2017)

Cover image

A molecular dynamics simulation of liquid crystal elastomers, Proceedings of the Royal Society A 477, issue 2253, September 2021

ECMI blog posts

Electromechanical Energy Conversion via Liquid Crystal Elastomers (October 2024)

I am a fellow of the UK Higher Education Academy. Over the years, I have contributed to the professional development of many young people through teaching, supervision, collaboration and mentoring.

Courses taught

Introduction to Mathematical Modelling of Liquid Crystal Elastomers
- PhD-level Mathematics (2023 - 2024)
Numerical Analysis
- Year 2 Mathematics (2013 - Present)
Finite Elasticity
- Year 3 Mathematics (2020 - 2022)
- Year 4 MMath (2015 - 2020)
Classical Mechanics
- Year 1 Mathematics (2012 - 2017)

I offer a range of projects to final year undergraduate students and to year 12 students on Nuffield Research Placements and Experiences Programme.

Career overview

I started my mathematical journey as an undergraduate student at the University of Bucharest, Romania. I later continued my studies with a Part III of the Mathematical Tripos at the University of Cambridge, UK, funded by a full Shell Centenary Scholarship awarded by Shell Group and Cambridge University Trust. In 2005, I earned my PhD for research in numerical analysis from the University of Durham, UK. I then expanded my expertise as a postdoctoral researcher at the Universities of Strathclyde, Cambridge, and Oxford, focusing on mathematics and mechanics of solids, where there was a need for mathematicians to specialise in this key interdisciplinary field. I joined Cardiff University as a Lecturer in 2011 and steadily progressed to my current academic role.

Honours and awards

Fellow of the Institute of Mathematics and Its Applications (2024)
Cardiff University Outstanding Contribution Award (2015)

Professional memberships

Society for Industrial and Applied Mathematics (SIAM)
- Vice President of SIAM-UKIE Section (2023 - 2025)
- Secretary & Treasurer of SIAM-UKIE Section (2014 - 2016)
  - Cambridge Hosts 20th Anniversary Meeting of the UKIE SIAM Section (2016)
  - SIAM-UKIE New Media to Help Increase Impact of Members' Activities in the Wider Community (2014)
- Faculty Adviser of SIAM-IMA Student Chapter at Cardiff University
  - SIAM-UKIE National Student Chapter Conference (2024)
  - Cardiff Students Hold First SIAM Chapter Day (2013)
The International Society for the Interaction of Mechanics and Mathematics (ISIMM)
The British Liquid Crystal Society (BLCS)

Committees and reviewing

Associate Editor
- Journal of Elasticity: The Physical and Mathematical Science of Solids (Springer)
  - Special Issue on Liquid Crystal Elastomers and Their Theory (2026)
- Mathematics and Mechanics of Solids (SAGE)
  - Special Issue Honouring Alain Goriely FRS (2024)
Member of Editorial Advisory Board
- International Journal of Non-Linear Mechanics (Elsevier)
Member of Editorial Board
- Mechanics of Soft Materials (Springer)
Research Councils Services
- EPSRC Peer Review College
- UKRI Talent P College

Postdoctoral researchers

Dr Yang Liu, Research fellow, HORIZON-MSCA-2022 (2023-2025)
Dr Thomas Raistrick, Research associate, EP/S028870/1 (2022)
Dr Maciej Buze, Research associate, EP/S028870/1 (2019 - 2022)
Dr Hayley Wyatt, Research associate, EP/M011992/1 (2015 - 2017)
- First Soapbox Science in Cardiff

Current supervision

Rabin Poudel

Past projects

Dr Manal Alamoudi, PhD thesis (2018 - 2022)
Dr Danielle Fitt, PhD thesis (2018 - 2021)
Dr Alexander Safar, PhD thesis (2015 - 2019)
- UK Association for Computational Mechanics Mike Crisfield Prize (2017)
Dr Khulud Alayyash, PhD thesis (2013 - 2017)

Contact Details

Abacws, Room 5.14, Senghennydd Road, Cathays, Cardiff, CF24 4AG

Research themes

Specialisms

Applied mathematics
Materials modelling
Scientific computing
Soft matter

Director of Research co-leads second retreat for women in applied mathematics